GPS Solutions

Vehicular attitude can be estimated using micro-electro-mechanical systems (MEMS) based magnetic, angular rate, and gravity (MARG) sensors or global navigation satellite systems (GNSS). In challenging environments external accelerations, magnetic distortions, and failure of GNSS will result in significant attitude estimation errors. We proposed a hybrid attitude estimation algorithm based on the low-cost dual-antenna GNSS/MEMS MARG sensor integration, in which the two GNSS antennas are connected to two separate low-cost receivers. Heading and pitch angles are obtained from the moving baseline spanned by the two antennas. An error state Kalman filter is built for data fusion, the filter shares the identical kinematic model but switches the measurement model according to the valid aiding sources. Six possible measurement update schemes are conditioned on the availability of GNSS-derived angles and the disturbances detected in the MARG sensor data. The accuracy degradation of attitude estimation caused by disturbances is alleviated by adjusting the measurement covariance matrix adaptively. A land vehicle-based dynamic experiment was performed to assess the proposed algorithm. Compared to the MARG sensor alone method, the root mean square errors of the proposed GNSS/MARG sensor integrated method were reduced by 38.9%, 65.8%, and 45.6% in the roll, pitch, and yaw angles, respectively.

Atmospheric weighted mean temperature (Tm) is pivotal for converting zenith wet delay (ZWD) derived from global navigation satellite system (GNSS) signal to precipitable water vapor (PWV). Currently, most Tm models are developed based on radiosonde (RS) data or reanalysis data. These models are limited by the availability of measured surface temperature and the accuracy of input data used during modeling. Additionally, they face challenges in accounting for the diurnal effect on Tm. In this study, we innovatively use the latest AI weather model, Pangu-Weather, to estimate surface air temperature (Pangu-Ts) in 2016–2019. Compared with the measured surface temperature (RS-Ts) at RS stations, bias and root mean square error (RMSE) are − 0.75 K and 2.54 K, respectively. Subsequently, a Tm forecast model (RF-Tm) in China is developed based on this data using random forest (RF). The model only requires the input of time, 3D coordinates of stations, and predicted Pangu-Ts data to yield the forecasted Tm estimates. The validation results based on RS data show that bias of the RF-Tm is − 0.38 K and the RMSE is 2.47 K. Through comparison and validation with the Bevis model, GPT3, and the Tm forecast model (BP-Tm) developed using back propagation neural network (BPNN), RF-Tm demonstrates reductions in RMSE of 41.33%, 39.46%, and 2.76%, respectively. The mean values with theoretical RMSE and relative error of PWV derived from the RF-Tm are 0.171 mm and 0.90%. The RF-Tm proposed in this study can provide reliable and high-precision Tm estimation for real-time GNSS PWV retrieval.

Jamming of Global Navigation Satellite System (GNSS) signals severely affects the security of critical infrastructures and applications. The localization of intentional jamming sources, jammers, is an important step in securing GNSS resilience as it provides the authorities with technical tools to prevent the jamming. However, jammers are difficult to localize in dense urban areas because the existence of multipath and non-line-of-sight propagation challenges conventional methods significantly. This challenge has not been comprehensively addressed in previous research. Motivated by this gap, a ray-tracing tool using 3-D city models is established to simulate jamming signal propagation with high precision and thereby augment the existing signal simulators, and measurements for localization are modeled by characterizing a commercial GNSS receiver under jamming conditions. Then, we propose a novel two-step strategy which consists of an ensemble subspace k-Nearest-Neighbor (KNN) as a raw-predictor and an improved gravitational searching algorithm (GSA) as a fine-optimizer. Based on this, two cloud-computing-based schemes using signal-matching and joint-localization in fine-optimizing stage are proposed. Finally, the proposed methods are evaluated in three typical urban areas, and their effectiveness and superiority over conventional least-squares method based on an empirical path-loss model are validated.

The accuracy of satellite clock bias (SCB) directly affects the precision and reliability of positioning in Global Navigation Satellite System. Through precise clock bias prediction, positioning errors can be effectively reduced, and the overall reliability of the system can be improved. This paper proposes a deep learning model for SCB prediction based on the fusion of the Beluga Whale Optimization (BWO), Convolutional Neural Network (CNN), Bidirectional Gated Recurrent Unit (BiGRU), and an attention mechanism. The CNN is utilized to extract the spatiotemporal characteristic information from the clock bias sequence, while the BiGRU fully extracts relevant features through forward and backward propagation. The introduction of an attention mechanism aims to preserve essential features within the clock bias sequence to enhance feature extraction by both CNN and BiGRU networks. Additionally, the BWO is employed to optimize parameter selection in order to improve model accuracy. Experimental verification demonstrates that for the BeiDou Navigation Satellite System’s hydrogen-maser atomic clocks, the predicted clock bias for 6 h, 3 days, and 15 days are 0.078 ns, 0.475 ns, and 2.130 ns respectively, superior to the CNN-BiGRU-Attention, CNN-BiGRU, BiGRU, GRU, LSTM, BP, Kalman filter and ARIMA models.

Currently, the susceptibility of Global Navigation Satellite System (GNSS) signals underscores the importance of accurate GNSS time spoofing detection as a critical research area. Traditional spoofing detection methods have limitations in applicability, while the current learning-based algorithms are only applicable to the judgment of collected data, which is difficult to apply to real-time detection. In this paper, a real-time spoofing detection framework based on feature processing is proposed. The approach involves feature integration and correlation coefficient screening on each epoch of multi-satellite data. Additionally, special standardization strategy is employed to enhance the feasibility of real-time application. In the experimental phase, apart from utilizing the open dataset, an experimental platform is developed to generate dual-system data for experimentation purposes. Compared with the traditional clock difference detection method, this algorithm improves the detection performance by about 25%. Furthermore, the framework proposed can improve the detection F1 score of basic machine learning models and greatly reduce the computation time by more than ten times. On most datasets, models incorporating the framework achieved F1 scores of more than 99% and average response times of less than 10 μs. In summary, this study provides an effective intelligent solution for the application of real-time receiver spoofing detection.

The development of Global Navigation Satellite Systems (GNSS) results in large spatial geodetic networks with a distinct range of accuracy. Thus, classification of the GNSS stations is needed to determine which stations are appropriate for geodetic applications. Additionally, advanced Machine Learning (ML) techniques have been proposed. However, ML algorithms may sometimes be less sensitive due to a lack of samples or anomalies in input data. Therefore, this study introduces an approach in which human-based supervision is integrated into ML processes to improve the ML model’s performance in classifying the continuous GNSS stations. The human factor influences the ML processes through two sampling strategies: “suggest-decide” and “correct-retrain”, where the accuracy of ML models will be improved via human-based corrections. The idea is that the unsupervised ML-based clustering techniques are driven by human-based supervision to create samples for training the supervised ML-based classification models. In this study, we develop a MATLAB app to automate the clustering and labeling processes. Our finding demonstrates that applying these sampling strategies can enhance the accuracy of the ML-based classification models from under 50 % up to \(\sim\) 99 % after re-training. Also, this study categorizes almost 9000 continuous monitoring stations in the Nevada database, of which 1900 stations in Europe serve as samples for training the ML-based classification models. Furthermore, the methodologies developed in this study can be applied to warning systems, which utilize internal and external human resources to correct errors, address unusual situations, and provide timely feedback for better performance of ML-based forecasts.

Displacement-based modal analysis has been proven to yield more robust and reliable modal parameter identification results compared to acceleration-based modal analysis. Global navigation satellite systems (GNSS) under real-time kinematic (RTK) mode is a widely used dynamic displacement monitoring technique. Notably, the monitoring accuracy of GNSS is limited due to the existence of multiple error sources such as multipath effect and satellite shielding effect. Particularly, blind source separation (BSS) can determine structural modal parameters from output-only responses. This method is advantageous compared with conventional modal analysis method because it does not require any prior knowledge of the structure. However, common BSS methodologies are susceptible to the local minima problem and are sensitive to low signal-to-noise ratio (SNR) signals. To address the aforementioned problems, this study first presents a combination filter strategy of Chebyshev and wavelet threshold (WT) to estimate the structural dynamic displacement based on GNSS RTK measurement. Then, a swarm-enhanced blind identification approach is proposed to determine structural modal parameters from the estimated displacement. The core of this approach is to develop a robust K-means clustering approach with swarm intelligence optimization to estimate the mixing matrix (i.e., mode shape matrix). Finally, the developed approach is verified in a four-degree-of-freedom numerical model and then implemented to a field test of a long-span cable-stayed bridge in engineering practice. The results illustrate that the designed combination filter can effectively weaken the influence of GNSS-RTK background noise while retaining the components related to structural dynamic vibration. Meanwhile, comparing with the conventional BSS approach (i.e., sparse component analysis), the developed swarm-enhanced blind identification approach exhibits higher robustness and convergence accuracy in determining structural modal parameters.

For about three decades, the Global Navigation Satellite System (GNSS) has been used for high-precision positioning in scientific and engineering applications, such as deformation monitoring for seismicity and volcano eruption. Such high-precision positioning applications require millimeter-level positioning accuracy. There are many man-made and natural reflective surfaces near the GNSS receiving antennas. GNSS signals can be reflected and then arrive at the GNSS antenna. The multipath effect occurs when the direct signal is mixed with the reflected signal at the GNSS receiver. Choke-ring antennas are designed to mitigate the multipath effect of reflected signals from below the horizontal plane of the GNSS receiving antenna. Moreover, GNSS receiving antennas at network/permanent stations are usually installed on tall pillars or monuments to prevent multipath from “ground” reflected signals. However, part of the reflected signals can still arrive at the GNSS antenna center and cause multipath errors in GNSS measurements. How much can the multipath effect be on the real-time GNSS-measured displacements in studies on seismicity and volcano eruption? This work investigates the below-the-horizon multipath effect of choke-ring antennas on GNSS carrier-phase measurements. Here we show the differenced carrier-phase multipath errors of two commonly used GNSS antennas at the International GNSS Service (IGS) tracking stations can reach 8 mm, the maximum, with the mean and SD in a few millimeters at the 95% confidence level. The findings of this work should be applicable to other choke-ring antennas with similar architecture.

The ambiguity resolution (AR) technology effectively accelerates convergence and improves precise point positioning (PPP) accuracy. Many observations involved in the calculation can enhance the accuracy of parameter estimation. Still, it can also introduce unmodeled errors, making it difficult to fix ambiguities, especially in multiple global navigation satellite system (GNSS). This paper presents a novel PPP Partial-AR (PAR) method to enhance Precise Point Positioning (PPP) performance by selecting an ambiguity subset based on the variation of ambiguity check factors, including the ratio, ambiguity dilution of precision (ADOP), and Bootstrapping success rate. The proposed method is validated using post-processing and real-time static and kinematic datasets across five GNSS integration modes involving the global positioning system (GPS) and BeiDou navigation satellite system (BDS), demonstrating that PPP Partial-AR (PAR) outperforms the method that fixes all ambiguities, known as PPP Full-AR (FAR). The static and kinematic post-processing experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 84.6 and 79.5% to 94.2 and 91.9%, decreases the time to first fix (TTFF) from 21.4 and 31.1 min to 17.7 and 25.4 min, and reduces the root mean square error (RMSE) from 12.7/11.3/32.2 and 21.7/19.4/51.8 mm to 11.5/10.3/30.9 and 19.1/18.1/48.9 mm in the north-east-up directions, respectively. The static and kinematic real-time experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 80.1 and 71.7% to 91.8 and 86.6%, decreases the TTFF from 29.5 and 35.5 min to 25.2 and 28.7 min, and reduces the RMS from 22.4/19.4/45.9 and 33.8/26.9/65.2 mm to 18.6/17.1/42.0 and 29.2/23.6/60.5 mm in the north-east-up directions, respectively. Moreover, the real-time experiments with actual kinematic data show that the proposed method significantly improves the ambiguity epoch fixing rate from 43.3% for PPP-FAR to 50.7% for PPP-PAR, and increases the positioning accuracy with an RMS value of 0.28/0.21/0.57 m for the PPP float solution, 0.23/0.19/0.55 m for the PPP-FAR solution towards 0.21/0.18/0.53 m for the PPP-PAR solution.

Although GNSS (Global Navigation Satellite System) is well-established for outdoor positioning, it still encounters challenges in urban occluded environments. Currently, multi-source fusion positioning has emerged as the primary solution. Since commonly used smartphones can simultaneously receive satellite signals and send 5G signals, researching GNSS/5G fusion positioning based on smartphones is a highly feasible solution. However, existing studies on GNSS/5G fusion positioning primarily rely on simulation data and TOA (Time of Arrival). On the one hand, simulation data often fail to accurately reflect positioning performance in real-world environments. On the other hand, while TOA often struggles to achieve high accuracy due to time synchronization errors, the AOA (Angle of Arrival) method, which does not depend on time synchronization, presents a promising alternative. Therefore, we propose a GNSS/5G tightly coupled fusion positioning method based on AOA measurements and conduct practical tests. For the first time, we use a smartphone to verify the performance of this method in urban occluded environments. The static experimental results indicate that SPP of the smartphone performs poorly in occluded environments. In contrast, AOA positioning demonstrates relatively stable performance. GNSS/5G fusion positioning yields the best positioning results, exhibiting a best improvement of 98.18% over SPP and 70.69% over AOA positioning. For the two dynamic routes with varying levels of occlusion, GNSS/5G fusion positioning shows considerable enhancements, achieving improvements of 39.39% and 9.32% over SPP, and 13.35% and 44.68% over AOA positioning. These results demonstrate that the fusion positioning method can effectively compensate for the shortcomings of satellite positioning in occluded environment.

Ionospheric scintillations disrupt the trans-ionospheric satellite signals and cause quandaries in satellite applications typically near the low equatorial sites; GNSS signals are utilized extensively for monitoring such anomalies. This work presents the unique results that confirm the suitability and limitations of a commercial low-cost, GNSS module (Ublox ZED F9P) for amplitude scintillation monitoring from a location in India situated near the EIA crest during the autumnal equinox of 2022 for low to intense amplitude scintillations. Comparison of amplitude scintillation index (S4) and fade rate using concurrent data from a Leica GR50 geodetic receiver and the low-cost module shows fairly good agreement between the results. The findings have practical utility in designing cost, size, and power-efficient GNSS probes using such modules for ionospheric research. Such modules are not a replacement for the traditional receivers but can be utilized to implement a multi-point, autonomous amplitude scintillation monitoring network.

Smartphone-based location-based services (LBS) require enhanced horizontal position accuracy with integrity. Due to the mass-market nature and compact design of smartphones, they utilize low-cost antennas and receivers, making them susceptible to multipath effects and other errors, which complicates the differentiation between reliable and unreliable measurements. To address these challenges, this paper explores the application of an adaptive Kalman filter technique to improve smartphone positioning accuracy. Adaptive Kalman filters adjust parameters such as process noise covariance or measurement noise covariance to modify the filter gain. When augmented with outlier detection mechanisms, the filter becomes more robust. This paper introduces a robust adaptive Kalman filter to enhance smartphone position accuracy. Outliers are detected using standardized innovations as a learning statistic, and a t-test is applied to these statistics to identify and mitigate outliers and adapt the measurement noise covariance accordingly. While previous research used empirical values for thresholds to adapt measurement noise covariance matrix, this study derives thresholds from t-tests, contingent on the normal distribution of learning statistics. By eliminating clock reset effects, innovations are transformed from bimodal to a normal distribution. Testing across multiple datasets demonstrates reductions of up to 42% in horizontal positioning root mean square error, with 50th, 68th, and 95th percentile statistics showing improvements of up to 53%, 41%, and 61%, respectively.

Groundwater withdrawal and recharge lead to changes in terrestrial hydrological loads, which in turn cause surface deformation. Based on poroelastic response and elastic loading theory, the 24 Global Positioning System (GPS) stations on the North China Plain (NCP) and the Gravity Recovery and Climate Experiment mission and its follow-on (GRACE/GRACE-FO) are first integrated to quantify the spatial–temporal changes in surface deformation and groundwater storage (GWS) during 2011–2022. The results show that the trends of GWS in the three periods of 2011–2017, 2018–2020, and 2021–2022 were  − 2.56 ± 0.33 mm/yr,  − 4.72 ± 1.74 mm/yr, and 11.76 ± 4.18 mm/yr, respectively. Most of the GPS stations showed a significant negative correlation between GWS and surface deformation under the elastic loading theory. In 2021, surface subsidence of more than 5 mm was experienced by 94% of the GPS stations, and 58% experienced more than 10 mm, further confirming that the South-to-North Water Diversion (SNWD) effectively replenishes groundwater resources in the NCP. The SNWD, precipitation, and human activity were the three principal factors influencing the groundwater in the NCP. SNWD effectively mitigated the continuous decrease of groundwater in the NCP.

Satellite signals from the Global Navigation Satellite System (GNSS) are refracted as they pass through the troposphere, owing to the variable density and composition of the atmosphere, causing tropospheric delay. Typically, tropospheric delay is treated as an unknown parameter in GNSS data processing. Given the growing need for real-time GNSS applications, accurate tropospheric delay predictions are crucial to improve Precise Point Positioning (PPP). In this paper, time-series of tomography data are used for wet refractivity prediction employing Machine Learning (ML) techniques in both Poland and California, under extreme weather conditions including sweeping rain bands and storms. The predicted wet refractivity is implemented for tropospheric delay determination through ray-tracing technique. PPP processing is conducted in both static and kinematic modes using different setups. These are: (1) common PPP, called Com-PPP, (2) Ray-PPP, which applies obtained tropospheric delay on GNSS observations and thus eliminates tropospheric parameters from unknowns, and (3) Dif-PPP, which applies the difference of estimated tropospheric delay from ray-tracing and GNSS measurements to compensate for the remaining tropospheric delay in the observations. The results show that Dif-PPP reduces the Mean Absolute Error (MAE) of the Three-Dimensional (3-D) component between 8 and 33% in static mode compared to the Com-PPP method. Additionally, it can improve the convergence time of the up component in the kinematic mode by between 6 and 17%.

The European Galileo High Accuracy Service (HAS) started to provide freely and openly accessible real-time precise satellite orbit, clock and code bias products to global users on January 24, 2023. Combined with the already running BeiDou PPP-B2b service, the launch of a variety of satellite-based PPP services provided more choices to users. However, different satellite-based PPP services provide services for different GNSS systems, which hamper users to make full use of multi-GNSS systems. Therefore, the combination of different satellite-based products can further improve the availability of corrections, usage of multi-GNSS observation data and positioning performance. This paper proposes to combine HAS and PPP-B2b products by the Helmert coordinate transformation method. To validate the algorithm, HAS and PPP-B2b products of day of year (DOY) 308–317 in 2023 were collected in Zhengzhou, China. First, they are evaluated in terms of correction availability, orbit and clock quality. Then the HAS and PPP-B2b products are combined by the Helmert coordinate transformation method. Two combination strategies are proposed. The first strategy is integrating BDS satellites of PPP-B2b products into HAS products (denoted as C_H), while the second strategy is integrating Galileo satellites of HAS products into PPP-B2b products (denoted as C_B). Finally, the combined strategies are evaluated with static and kinematic data. Based on the static data of 18 Multi-GNSS Experiment (MGEX) stations in China and its surrounding areas, the results show that, when separately using HAS and PPP-B2b products for PPP, the average accuracy in horizontal and vertical directions are (2.4, 2.7 cm) and (2.4, 2.0 cm), respectively. The average accuracy of C_H strategy is 2.1 and 1.7 cm, which was improved by 31.3% compared with separately using the products. Similarly, the average accuracy of C_B strategy is 2.1 and 1.9 cm, corresponding to improvements of 29.6%. When comparing the two combined strategies, it is noted that the C_B strategy converges faster. Based on the data from vehicle platform, the results show that the horizontal and vertical accuracy of the C_B strategy is 8.6 and 15.7 cm respectively. The accuracy improvement of C_B is better than that of C_H strategy, and the average accuracy is 68.4% better than that of separately using the products. The above results show that the two combined strategies can improve positioning accuracy. In addition, the improvements in accuracy and convergence speed of C_B strategy are more significant. Users are advised to use C_B strategy for the combination of HAS and PPP-B2b products, which will greatly expand the application of HAS and PPP-B2b services.

In recent decades, Global Navigation Satellite System-Interferometric Reflectometry (GNSS-IR) environmental parameters inversion has become a research hotspot in the field of GNSS. Among them, sea/water level inversion has become one of the applications with better inversion performance because of its clear mathematical relationship and horizontal reflection surface. Among the many sources of error in GNSS-IR sea level inversion, sea surface height variation is the most significant source of error. The key to correcting this error is the accurate estimation of the rate of change of sea surface height. However, the estimation of the rate of change is difficult to be accurate, making it difficult to correct this error precisely. Theoretically, the retrieval error results in an offset in the initial phase parameter in the signal-to-noise ratios (SNR) oscillation sequence. Therefore, the error can also be corrected by estimating the phase. However, the phase determined during parameter fitting is between − π and π. When the error affects the phase offset magnitude greater than 2π, the integer cycle of it is not available, resulting in the phase-based correction model not being able to correct the error. In other words, the integer cycle ambiguity that exists in GNSS positioning also exists in SNR phase determination. In this article, a method for integer cycle determination based on the assistance of the traditional sea surface height variation error model is proposed, and an error correction method based on SNR phase and a multi-mode multi-frequency combination inversion method are also proposed. Two GNSS sites with different tidal amplitudes are selected to carry out the experiments. The results show that the phase-based error correction method improves the sea-level retrieval accuracy by about twice as much as that obtained using the traditional correction method. Meanwhile, this paper analyses the adaptability of the phase-based error correction method: good results can be achieved in the lower elevation angle interval, while the results are poor in the higher elevation angle interval. This study provides another solution idea for GNSS-IR error correction based on phase parameters, and the accuracy improvement achieved by this method is significant.

The least squares method is still commonly employed in traditional global navigation satellite system (GNSS) velocity estimation, but this method is easily biased by outliers from various sources. Random sample consensus (RANSAC) and solution separation (SS) algorithms have been employed in the domain of GNSS velocity estimation to identify and eliminate faults in the GNSS propagation process, yielding favorable outcomes. However, these algorithms are generally applied in single-epoch velocity estimation applications and use a single threshold for inspection and elimination, lacking adaptability to the observation environment. Therefore, a residual-based multithreshold constraint algorithm (RMCA) is proposed to improve the iterative results and obtain a time series solution of the GNSS velocity model. In the RMCA, the importance of residuals in the least squares approach is considered, and errors are directly expressed. Second, rather than employing a predetermined single threshold for exclusion, flexible threshold regulation is applied across various levels. Finally, the RMCA leverages the historically optimized velocity to establish sensible constraints on the current velocity estimation. Moreover, a mutual detection mechanism between GNSS velocity models is established. An experimental analysis of two groups of urban vehicles reveals that the velocity results obtained via the RMCA are more robust than those obtained via the traditional least squares algorithm and the SS scheme and are more continuous than those obtained via RANSAC. The RMCA is evidently well designed and efficient, demonstrating significant application value.